oo Sprint 1051 PM sessionmasteringphysicscom C Item 6 Master

oo Sprint 10:51 PM session.masteringphysics.com C Item 6 MasteringPhysics Item 6 Dan is gliding on his skateboard at 3.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 6.0 m/s (as measured by an observer on the ground). Dan\'s mass is 40 kg and the skateboard\'s mass is 6.0 kg Part A How fast is Dan going as his feet hit the ground? Express your answer using two significant figures. m/s Submit Give Up Give OP Incorrect; One attempt remaining; Try Again Continue >

Solution

As Dan is moving on the skateboard, he along with the skateboard has some linear momentum along the direction of their motion.

This momentum is given as: (M + m)u where M is the mass of Dan, m is the mass of the skateboard and u is the initial velocity of both of them.

Now, as Dan jumps backwards, he imparts a final velocity of, say, v = 6 m/s forward with respect to the ground and himself attains a velocity backwards, say V m/s.

We will use the principle of conservation of linear momentum to form an equation involving the speed of Dan and then resolve to find the required value.

That is, Initial Linear momentum = Final linear momentum

or, (M+ m)u = MV + mv

or, 46 x 3 = 40V + 6 x 6

or, 40 V = 102

Hence, V = 2.55 m/s

Therefore Dan will hit the ground with the speed of 2.55 m/s